Refitting solutions promoted by $\ell_{12}$ sparse analysis regularization with block penalties

Abstract : In inverse problems, the use of an $\ell_{12}$ analysis regularizer induces a bias in the estimated solution. We propose a general refitting framework for removing this artifact while keeping information of interest contained in the biased solution. This is done through the use of refitting block penalties that only act on the co-support of the estimation. Based on an analysis of related works in the literature, we propose a new penalty that is well suited for refitting purposes. We also present an efficient algorithmic method to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty. Experiments illustrate the good behavior of the proposed block penalty for refitting.
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Contributor : Nicolas Papadakis <>
Submitted on : Wednesday, March 6, 2019 - 12:27:29 PM
Last modification on : Friday, March 29, 2019 - 11:26:16 AM

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  • HAL Id : hal-02059006, version 1
  • ARXIV : 1903.00741

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Charles-Alban Deledalle, Nicolas Papadakis, Joseph Salmon, Samuel Vaiter. Refitting solutions promoted by $\ell_{12}$ sparse analysis regularization with block penalties. International Conference on Scale Space and Variational Methods in Computer Vision, Jun 2019, Hofgeismar, Germany. 〈hal-02059006〉

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